I have these type of "bleeds" a lot of the time. The word "bleed" really makes it sound scarey, but mine happens so often that I am very used to it now. You say though that yours has not been diagnosed as subcon.haem.
The usual causes of this type of problem include coughing, sneezing, heavy lifting and straining or mild ocular trauma (just simply rubbing of the eye while sleeping). The source of the blood is usually a small, normal blood vessel which was stressed and ruptured. The condition is never associated with a decrease in vision or significant pain and discomfort. The presence of these symptoms suggest a more serious problem which requires urgent attention.
Only a small amount of blood is required, significantly less than one drop, to produce a nasty looking eye. So, unless the vision is decreased, the eye is painful or the hemorrhages are recurrent, there is no need to further evaluate patients with this common problem.
The other types of this common complaint are:-
"Rapid onset red eye with pain"
infection / inflamation
acute closed angle glaucoma
"Red eye with mild or no pain"
dry eye / keratitis
eyelash problems / blepharitis
systemic drug reaction
lumps and bumps
"Contact lens related red eyes"
I have Sjogren's, which does cause a lot of dryness. Consequently I then rub my eyes (I shouldn't I know) and then this causes redness for me. Have they looked into Sjogren's for you?
I am quite concerned for you that the doctors you have spoken to have not taken it any further. It does need more investigation I feel.
Hope this helps a bit.